Randell Heyman

activity

20132023

most citedHyperbolic summation for functions of the GCD and LCM of several integers

11 citations · 29 across the 16 of their papers we have counts for

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math.NT2013

On the number of polynomials of bounded height that satisfy Dumas's criterion

Randell Heyman

We study integer coefficient polynomials of fixed degree and maximum height $H$ , that are irreducible by Dumas's criterion. We call such polynomials Dumas polynomials. We derive up…

math.NT2013★ 4 cited

Pairwise non-coprimality of triples

Randell Heyman

We say that $(a_{1}, ..., a_{k})$ is pairwise non-coprime if $g cd (a_{i}, a_{j}) \neq = 1$ for all $1 \leq i < j \leq k$ . Let $a_{1}, a_{2}, a_{3}$ be positive integers less than $H$ . We obtain an asymptot…

math.NT2013

On Shifted Eisenstein Polynomials

Randell Heyman, Igor E. Shparlinski

We study polynomials with integer coefficients which become Eisenstein polynomials after the additive shift of a variable. We call such polynomials shifted Eisenstein polynomials.…

math.NT2013★ 2 cited

On the Number of Eisenstein Polynomials of Bounded Height

Randell Heyman, Igor E. Shparlinski

We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree $d$ and of height at most $H$ , as $H\to \inf…